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In this paper we develop empirical measures for the strength of spillover effects. Modifying and extending the framework by Diebold and Yilmaz (2011), we quantify spillovers between sovereign credit markets and banks in the euro area. Spillovers are estimated recursively from a vector autoregressive model of daily CDS spread changes, with exogenous common factors. We account for interdependencies between sovereign and bank CDS spreads and we derive generalised impulse response functions. Specifically, we assess the systemic effect of an unexpected shock to the creditworthiness of a particular sovereign or country-specific bank index to other sovereign or bank CDSs between October 2009 and July 2012. Channels of transmission from or to sovereigns and banks are aggregated as a Contagion index (CI). This index is disentangled into four components, the average potential spillover: i) amongst sovereigns, ii) amongst banks, iii) from sovereigns to banks, and iv) vice-versa. We highlight the impact of policy-related events along the different components of the contagion index. The systemic contribution of each sovereign or banking group is quantified as the net spillover weight in the total net-spillover measure. Finally, the captured time-varying interdependence between banks and sovereigns emphasises the evolution of their strong nexus.